Finite Group Databasebeta

← #14518854

Subgroups — #14518854

Order 1944.

532 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 532 conjugacy classes of subgroups — too many to draw. Only its 63 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3⋊#4208C211yesmaximal, characteristic, complemented
2C2×C3⋊#4207C211yesmaximal, characteristic, complemented
3C3×#66409C211yesmaximal, characteristic, complemented
4#10619909—33nomaximal
5#10619899—31nomaximal
6#10619887—31nomaximal
7#10619878—31nomaximal
8C2×C3×#737C2211yescharacteristic
9C3⋊#4208—21no—
10C3⋊#4207—21no—
11C2×C3⋊#272D311yescharacteristic
12C2×C3⋊(C3⋊D9)D311yescharacteristic, complemented
13C2×#4208—33no—
14C2×#4208—63no—
15C2×#4207—33no—
16C2×#4207—63no—
17C2×C3⋊AGL(1,ℤ/9)—61no—
18C2×C3⋊((C3⋊D3)⋊C3)—31no—
19C2×C9×C3⋊D3—31no—
20C2×C9×C3⋊D3—31no—
21C2×C9×C3⋊D3—61no—
22C2×C3×C3⋊D9—31no—
23#66409D313yescomplemented
24C3×C3⋊Dic9D311yescharacteristic, complemented
25C3×3−1+2⋊C4—61no—
26C3×(C3⋊Dic3)⋊C3—31no—
27C32×Dic9—31no—
28C3×#737D411yescharacteristic, complemented, Sylow
29#6295—91no—
30#6292—91no—
31#6200—93no—
32#6195—93no—
33#6195—91no—
34#6194—91no—
35C2×#737—23no—
36C2×#737—23no—
37C2×#737—43no—
38C2×#737C2×D313yes—
39C2×C3×3−1+2—21no—
40C2×C3×3−1+2—21no—
41C2×C3×3−1+2—41no—
42C2×C3×H(3,𝔽3)C2×D311yescharacteristic
43C2×C32×C9—21no—
44C2×C32×C9C2×D311yescharacteristic
45C2×C32×C9C2×D311yescharacteristic
46C3⋊#272—21no—
47C3⋊(C3⋊D9)—21no—
48#4208—66no—
49#4208—63no—
50#4207—66no—
51#4207—63no—
52C3⋊AGL(1,ℤ/9)—62no—
53C3⋊((C3⋊D3)⋊C3)—61no—
54C9×C3⋊D3—62no—
55C9×C3⋊D3—61no—
56C9×C3⋊D3—61no—
57C3×C3⋊D9—61no—
58C2×C3⋊(C3⋊D3)—31no—
59C2×C3×C3⋊D3—31no—
60C2×C3×C3⋊D3—31no—
61C2×C3×C3⋊D3—61no—
62C2×C3×C3⋊D3—91no—
63C3×C3⋊Dic3—31no—
64C32×Dic3—91no—
65C2×#272—33no—
66C2×#272—63no—
67C2×C3⋊D9—31no—
68C2×C3⋊D9—33no—
69C2×C3⋊D9—61no—
70C2×C3⋊D9—63no—
71C2×AGL(1,ℤ/9)—183no—
72C2×(C3⋊D3)⋊C3—93no—
73C2×D3×C9—91no—
74C2×D3×C9—93no—
75C2×D3×C9—91no—
76C2×D3×C9—181no—
77C2×D3×C9—183no—
78C2×C3×D9—91no—
79C2×C3×D9—181no—
80C3⋊Dic9C3⋊D311yescharacteristic, complemented
813−1+2⋊C4—63no—
82(C3⋊Dic3)⋊C3—33no—
83C3×Dic9—31no—
84C3×Dic9—33no—
85C3×Dic9—61no—
86#737—23no—
87#737—23no—
88#737—43no—
89#737D1213yescomplemented
90C3×3−1+2—21no—
91C3×3−1+2—21no—
92C3×3−1+2—41no—
93C3×H(3,𝔽3)#6711yescharacteristic
94C32×C9—21no—
95C32×C9D1211yescharacteristic, complemented
96C32×C9#6711yescharacteristic, complemented
97C4⋊(C3⋊D3)—271no—
98#626—273no—
99#626—271no—
100#626—271no—
101#625—271no—
102#611—271no—
103C2×C33—21no—
104C2×C33D3211yescharacteristic
105C2×C33D3211yescharacteristic
106C3⋊(C3⋊D3)—61no—
107C3×C3⋊D3—62no—
108C3×C3⋊D3—61no—
109C3×C3⋊D3—61no—
110C3×C3⋊D3—181no—
111C2×3−1+2—23no—
112C2×3−1+2—23no—
113C2×3−1+2—43no—
114C2×3−1+2—43no—
115C2×3−1+2—46no—
116C2×3−1+2—43no—
117C2×H(3,𝔽3)—23no—
118C2×H(3,𝔽3)D3213yes—
119C2×C3×C9—21no—
120C2×C3×C9—23no—
121C2×C3×C9—21no—
122C2×C3×C9—21no—
123C2×C3×C9—23no—
124C2×C3×C9—21no—
125C2×C3×C9—41no—
126C2×C3×C9—43no—
127C2×C3×C9—41no—
128C2×C3×C9D3211yescharacteristic
129C2×C3×C9D3213yes—
130C2×C3×C9C2×C3⋊D311yescharacteristic
131#272—66no—
132#272—63no—
133C3⋊D9—62no—
134C3⋊D9—66no—
135C3⋊D9—61no—
136C3⋊D9—63no—
137AGL(1,ℤ/9)—186no—
138(C3⋊D3)⋊C3—183no—
139D3×C9—186no—
140D3×C9—182no—
141D3×C9—181no—
142D3×C9—183no—
143D3×C9—181no—
144C3×D9—182no—
145C3×D9—181no—
146C2×C3⋊D3—31no—
147C2×C3⋊D3—31no—
148C2×C3⋊D3—61no—
149C2×C3⋊D3—91no—
150C2×C3⋊D3—93no—
151C2×C3⋊D3—271no—
152C2×C3⋊D3—541no—
153C2×C3×D3—91no—
154C2×C3×D3—93no—
155C2×C3×D3—91no—
156C2×C3×D3—183no—
157C2×C3×D3—181no—
158C2×C3×D3—271no—
159C2×C3×D3—271no—
160C2×C3×D3—541no—
161C32×C4—271no—
162C3⋊Dic3—31no—
163C3×Dic3—91no—
164C3×Dic3—93no—
165C3×Dic3—271no—
166C22×C9—271no—
167C2×D9—91no—
168C2×D9—181no—
169C2×D9—183no—
170Dic9—31no—
171Dic9—61no—
172C33—21no—
173C33#62511yescharacteristic
174C33#62611yescharacteristic
1753−1+2—23no—
1763−1+2—23no—
1773−1+2—43no—
1783−1+2—43no—
1793−1+2—46no—
1803−1+2—43no—
181H(3,𝔽3)—23no—
182H(3,𝔽3)#62613yes—
183C3×C9—21no—
184C3×C9—23no—
185C3×C9—21no—
186C3×C9—21no—
187C3×C9—23no—
188C3×C9—21no—
189C3×C9—41no—
190C3×C9—43no—
191C3×C9—41no—
192C3×C9#62611yescharacteristic
193C3×C9#62613yescomplemented
194C3×C9C4⋊(C3⋊D3)11yescharacteristic, complemented
195#67—811no—
196#67—811no—
197D12—811no—
198D12—813no—
199C2×C32—21no—
200C2×C32—23no—
201C2×C32—31no—
202C2×C32—31no—
203C2×C32—61no—
204C2×C32—61no—
205C2×C32—61no—
206C2×C32—121no—
207C2×C32D3×C3⋊D311yescharacteristic
208C2×C32#111311yescharacteristic
209C2×C32#111313yes—
210C3⋊D3—61no—
211C3⋊D3—61no—
212C3⋊D3—62no—
213C3⋊D3—181no—
214C3⋊D3—183no—
215C3⋊D3—541no—
216C3⋊D3—542no—
217C3×D3—182no—
218C3×D3—186no—
219C3×D3—181no—
220C3×D3—183no—
221C3×D3—181no—
222C3×D3—541no—
223C3×D3—542no—
224C3×D3—541no—
225C2×C9—21no—
226C2×C9—23no—
227C2×C9—21no—
228C2×C9—41no—
229C2×C9—43no—
230C2×C9—541no—
231C2×C9D3×C3⋊D311yescharacteristic
232D9—182no—
233D9—186no—
234D9—181no—
235C22×C3—271no—
236C22×C3—811no—
237C2×D3—93no—
238C2×D3—91no—
239C2×D3—91no—
240C2×D3—181no—
241C2×D3—183no—
242C2×D3—271no—
243C2×D3—271no—
244C2×D3—541no—
245C2×D3—813no—
246C3×C4—273no—
247C3×C4—271no—
248Dic3—91no—
249Dic3—271no—
250C32—21no—
251C32—23no—
252C32—31no—
253C32—31no—
254C32—61no—
255C32—61no—
256C32—61no—
257C32—121no—
258C32#629211yescharacteristic
259C32#629511yescharacteristic
260C32#629513yes—
261C9—21no—
262C9—23no—
263C9—21no—
264C9—41no—
265C9—43no—
266C9#629211yescharacteristic
267D4—2431noSylow
268C2×C3—21no—
269C2×C3—31no—
270C2×C3—33no—
271C2×C3—61no—
272C2×C3—63no—
273C2×C3—541no—
274C2×C3—1621no—
275C2×C3#4207⋊C211yescharacteristic
276C2×C3C3⋊#111311yescharacteristic
277D3—183no—
278D3—181no—
279D3—182no—
280D3—186no—
281D3—181no—
282D3—542no—
283D3—541no—
284D3—541no—
285D3—1623no—
286C22—271no—
287C22—811no—
288C4—271no—
289C3—21no—
290C3—33no—
291C3—31no—
292C3—61no—
293C3—63no—
294C3#1061990911yescharacteristic, complemented
295C3#1062015611yescharacteristic
296C2—541no—
297C2—1621no—
298C2#4207⋊D311yescharacteristic
subgroupG/H
center, hypercenterC2#4207⋊D3
commutator, Fitting, cosocleC2×C3×#737C22
FrattiniC2×C3C3⋊#1113
socleC2×C32#1113
hypocenterC3×#737D4
LCSG ▷ C2×C3×#737 ▷ C3×#737
UCSC1 ◁ C2

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C3⋊#4208C2semidirect
2. C2×C3⋊#4207C2semidirect
3. C3×#66409C2semidirect
12. C2×C3⋊(C3⋊D9)D3semidirect
23. #66409D3semidirect
24. C3×C3⋊Dic9D3semidirect
28. C3×#737D4semidirect
80. C3⋊Dic9C3⋊D3semidirect
89. #737D12semidirect
95. C32×C9D12semidirect
96. C32×C9#67semidirect
193. C3×C9#626semidirect
194. C3×C9C4⋊(C3⋊D3)semidirect
294. C3#10619909semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C3⋊#42082
C2×C3⋊#42072
C3×#664092
#106199093
#106198993
#106198873
#106198783